Simplify square root 108x^5y^6

√ 108x^5y^6

First, break up √108:

√108 = √4 x √27 = 2 x √3 x √9 = 2 x √3 x 3 = 6 √3

Since the x^5 is under a root of 2, that means we can take out an x^2 and leave one x under the radical:

√x^5 = x^2 (√x)

Since the y^6 is raised to an even power and the root is even (2), that means we can take out all of the y's without leaving any under the radical:

√y^6 = y^3

Now, combine all of our simplified forms into one expression:

6x^2y^3 √3x